

A296873


Numbers n whose base7 digits d(m), d(m1), ..., d(0) have #(pits) = #(peaks); see Comments.


4



1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 56, 57, 58, 59, 60, 61, 62, 65, 66, 67, 68, 69, 73, 74, 75, 76, 81, 82
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OFFSET

1,2


COMMENTS

A pit is an index i such that d(i1) > d(i) < d(i+1); a peak is an index i such that d(i1) < d(i) > d(i+1). The sequences A296873A296875 partition the natural numbers. See the guides at A296882 and A296712.


LINKS

Clark Kimberling, Table of n, a(n) for n = 1..9999


EXAMPLE

The base7 digits of 82 are 1,4,5; here #(pits) = 0 and #(peaks) = 0, so that 82 is in the sequence.


MATHEMATICA

z = 200; b = 7;
d[n_] := Differences[Sign[Differences[IntegerDigits[n, b]]]];
Select[Range [z], Count[d[#], 2] == Count[d[#], 2] &] (* A296873 *)
Select[Range [z], Count[d[#], 2] < Count[d[#], 2] &] (* A296874 *)
Select[Range [z], Count[d[#], 2] > Count[d[#], 2] &] (* A296875 *)


CROSSREFS

Cf. A296882, A296712, A296874, A296875.
Sequence in context: A272554 A179797 A268200 * A044923 A180925 A272302
Adjacent sequences: A296870 A296871 A296872 * A296874 A296875 A296876


KEYWORD

nonn,base,easy


AUTHOR

Clark Kimberling, Jan 09 2018


STATUS

approved



